Synth training - Migratory policy and violence in Chile

Setup

#install.packages("Synth")
#install.packages("ggplot2")
#install.packages("skimr")
#install.packages("dplyr")
#install.packages("knitr")
library(Synth)

##
## Synth Package: Implements Synthetic Control Methods.

## See https://web.stanford.edu/~jhain/synthpage.html for additional information.

library(skimr)
library(ggplot2)
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

library(htmltools)
library(knitr)

Motivation

There is a strong sense of insecurity in Chile

Which is backed up by the late figures on violence

Often, insecurity is attributed to migration without much evidence, leading to political repercusions

Local politicians target the 2019 policy to ease entry of Venezuelan migrants

Data exploration

southamerica <- read.csv("southamerica.csv")

Variable description

• country: country label for each observation.

• country_id: a numeric label for each country.

• year year of observation.

• hdi: human development index in year t.

• gini: gini coefficient in year t.

• hom: homicides per 1000,000 people in year t.

• ppincppp: GDP per capita, PPP (current international $) in year t.

• pov: poverty headcount ratio at $6.85 a day (2017 PPP) (% of population) in year t.

• homale: homicides of males per 1000,000 people in year t.

• linc: natural logarithm of variable ‘ppincppp’.

• lhom: natural logarithm of variable ‘hom’.

• lhomale: natural logarithm of variable ‘homale’

Summary statistics

skim(southamerica)

Data summary

Name	southamerica
Number of rows	384
Number of columns	12
_______________________
Column type frequency:
character	1
numeric	11
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
country	0	1	4	9	0	12	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
year	0	1	2005.50	9.25	1990.00	1997.75	2005.50	2013.25	2021.00	▇▇▇▇▇
hdi	0	1	0.71	0.07	0.51	0.66	0.71	0.76	0.86	▁▃▇▇▃
gini	0	1	50.31	5.47	39.50	45.23	50.12	54.72	61.60	▃▇▅▆▅
hom	0	1	16.59	15.26	0.97	6.18	12.16	20.84	85.43	▇▂▁▁▁
ppincppp	0	1	10908.37	5398.27	2294.73	6828.28	10114.63	14038.47	28337.07	▇▇▃▂▁
pov	0	1	35.14	25.61	-216.05	22.46	39.12	48.16	94.63	▁▁▁▅▇
homale	0	1	29.42	28.90	3.76	10.21	19.52	38.37	159.00	▇▂▁▁▁
country_id	0	1	6.50	3.46	1.00	3.75	6.50	9.25	12.00	▇▅▅▅▇
linc	0	1	9.17	0.52	7.74	8.83	9.22	9.55	10.25	▁▃▇▇▃
lhom	0	1	2.47	0.82	-0.03	1.82	2.50	3.04	4.45	▁▅▇▇▂
lhomale	0	1	3.00	0.87	1.32	2.32	2.97	3.65	5.07	▅▇▇▅▂

Crime trends measured by homicides per 100,000 people

Trends in South America

total_hom_by_year <- southamerica %>%
  group_by(year) %>%
  summarize(total_hom = sum(hom))

ggplot(total_hom_by_year, aes(x = year, y = total_hom)) +
  geom_line() +
  labs(title = "Total Homicides per 100,000 People (1990-2021)",
       x = "Year",
       y = "Total Homicides per 100,000 People")

ggplot(southamerica, aes(x = year, y = hom, group = country, color = country)) +
  geom_line() +
  labs(title = "Homicides per 100,000 in South American Countries (1990-2021)",
       x = "Year",
       y = "Ln Homicides per 100,000 people") +
  theme_minimal()

ggplot(southamerica, aes(x = year, y = homale, group = country, color = country)) +
  geom_line() +
  labs(title = "Homicides of males per 100,000 in South American Countries (1990-2021)",
       x = "Year",
       y = "Ln Homicides of males per 100,000 people") +
  theme_minimal()

Chile show an increase in homicide in recent years

chl_flt <- southamerica %>% filter(country == "Chile")

ggplot(chl_flt, aes(x = year, y = hom, group = country, color = country)) +
  geom_line() +
  labs(title = "Homicides per 100,000 in Chile (1990-2021)",
       x = "Year",
       y = "Ln Homicides per 100,000 people") +
  theme_minimal()

ggplot(chl_flt, aes(x = year, y = homale, group = country, color = country)) +
  geom_line() +
  labs(title = "Homicides of males per 100,000 in Chile (1990-2021)",
       x = "Year",
       y = "Ln Homicides of males per 100,000 people") +
  theme_minimal()

Synthetic control: Could the 2019 policy, and the consequent migration flow, be related to increasing violence in Chile?

Data prep

dataprep_out <- dataprep(
  foo = southamerica,
  predictors = c("hdi", "gini", "linc", "lhom"),
  special.predictors = list(
    list("homale", 1995, c("mean")),
    list("homale", 2000, c("mean")),
    list("homale", 2005, c("mean")),
    list("homale", 2010, c("mean")),
    list("homale", 2015, c("mean")),
    list("homale", 2020, c("mean"))
  ),
  dependent = "homale",
  unit.variable = "country_id",
  time.variable = "year",
  treatment.identifier = "Chile",
  controls.identifier = unique(southamerica$country[-which(southamerica$country == "Chile")]),
  time.predictors.prior = 1990:2019,
  time.optimize.ssr = 1990:2019,
  time.plot = 1990:2021,
  unit.names.variable = "country"
)

Applying Synth function

synth_out <- synth(
  data.prep.obj = dataprep_out
)

X1, X0, Z1, Z0 all come directly from dataprep object.


**************** 
 searching for synthetic control unit  
 

**************** 
**************** 
**************** 

MSPE (LOSS V): 10.52723 

solution.v:
 8.65439e-05 0.0003430499 7.15067e-05 0.0002399182 0.3025978 0.1872436 0.0545665 0.2092637 0.1334971 0.1120902 

solution.w:
 3.391e-07 0.06457197 3.04e-08 3.43e-08 6.7e-08 4.26e-08 1.043e-07 0.9354153 1.13958e-05 7.215e-07 1.07e-08 

Creating synthetic series

synth_chl <- dataprep_out$Y0 %*% synth_out$solution.w

Real vs synth

plot(
  1990:2021,
  dataprep_out$Y0 %*% synth_out$solution.w,
  type = "l",
  lty = "dashed", ylim = c(0,15))
lines(1990:2021,
      dataprep_out$Y1)

Gaps plot

gaps <- dataprep_out$Y1 - synth_chl

plot(
  1990:2021,
  gaps,
  type = "l"
)
abline(h=0, lty = "dotted")

Workflow

• Data collection from UN and World Bank datasets.

• Imputation of missing observations by country using MICE:

  • Method explanation here.

  • Python notebook with imputation code here.

• Data wrangling in Stata to create natural logarithm variables.

• Synthetic control done in R.

Limitations

• Lack of literature review.

• Imputation on MICE withouth any restriction. In some cases, some variables have only few observations.

• Potential collinearity, heteroskedasticity, and endogeneity.

• Poverty variable left outside the analysis as imputed values extremely high for some countries.

• Dependent variable accounts only for homicides of males but not for other crimes that could be helpful to analize: theft, drug related, organized crime.

• Limitation when interpreting Synth results.